Research On Propagation Mechanisms And Influence Characteristics Of Initial State Errors For Long-range Rocket

Alignment and leveling of an inertial navigation system are needed to provide the reference in inertial space before launching a long-range vehicle.The gravity model used in most present operational systems is based on a gravity field perpendicular to a reference ellipsoid,which approximates the mean-sea level equipotential surface called the geoid.Since the surface of the geoid deviat es from the reference ellipsoid,the gravity error also deviates in magnitude and direction.The deviation of the actual gravity magnitude from the reference value is known as the gravity anomaly,while the deviation of the gravity vector direction from th e reference ellipsoid normal is known as the vertical deflection.In addition,ballistic missile in mobile launch will also cause initial positioning errors,and collimation process will bring about launch azimuth deviation.The trajectory analysis,navigation and guidance calculation are generally ignored these initial state errors,thus resulting in the obvious flight state deviations and fall point deviations through dynamic equation.At present,with the improvement of the precision of inertial instruments,the influences of the instrumental errors are continuously declined.However,initial state errors as a kind of model error present obvious impact on fall point accuracy.In that case,research emphasis has been put on initial state errors in order to improve the hit accuracy.This dissertation is concerned with trajectory design,navigation calculation,guidance accuracy and error statistics properties caused by initial state errors.The major contents of this dissertation are consisted in the following parts.Firstly,formation mechanism of initial state errors is studied.Teasing out the initial state errors is an important premise of analyzing its impact regularities on trajectory design,navigation calculation and guidance accuracy.The accurate dynamical equations are established in launch inertial coordinate system and launch coordinate system,obtaining the influence expressions from initial state errors to accelerations.The initial error sources are classified and its propagation processes are hackled.The initial positioning errors,initial orientation errors and initial velocity errors show obviously influences on flight trajectory,and need to be considered in the subsequent error propagation,navigation and guidance.Secondly,the effect of initial state errors on trajectory parameters is studied.In current researches,the relative error of influence magnitude caused by initial state errors reaches the value of 10%,and the influence on the acceleration items of dynamical equation in launch coordinate system is not given,which will have an important influence on the accuracy of the trajectory parameters.In launch coordinate system,we establish the propagation equation of initial state errors on the basis of state space perturbation theory,and deduce the analytical expressions of gravitational acceleration deviation,Coriolis acceleration deviation and centrifugal acceleration deviation.Then,propagation matrices of engine-cutoff state deviations and fall point deviations are obtained.Through a variety of simulation scenarios,the trajectory parameters are obtained to analyze the propagation regularities of initial state errors,and the validity of the proposed high-accuracy analytical propagation model is verified.Thirdly,the influence property of initial state errors considering the coupling of apparent acceleration is studied.Because of the initial state errors,the navigation states solved by inertial navigation system(INS)are inevitably affected.In addition,initial state errors will affect the force of the missile,resulting in the change of flight altitude and velocity.Conversely,the calculation of thrust and aerodynamic force is related to the flight state.Therefore,a coupling effect between flight state and apparent acceleration will be formed,resulting in the apparent acceleration coupling deviation.Based on navigation equation,this paper analyzes the formation mechanism of navigation error caused by initial state errors when considering the apparent acceleration coupling.The navigation perturbation equation is established in launch inertial coordinate system based on state space perturbation theory.The apparent acceleration coupling deviation and initial velocity error are deduced.Analytical solutions of engine-cutoff navigation state deviations and fall point deviations are obtained when considering apparent acceleration coupling.A variety of simulation scenarios demonstrate the validity of the proposed analytical estimation model of navigation error,and estimation accuracy is effectively improved.The influence of initial state errors on navigation errors is analyzed and the corresponding conclusions are obtained.Subsequently,the influence of initial state errors on guidance accuracy is studied.Under the condition of initial state errors,the flight state output by navigation system is not the real state.Due to the navigation errors,guidance system receives the wrong guidance commands,which will bring about engine-cutoff state deviations and fall point deviations.This paper explicitly describes the relationship between nominal trajectory,uncontrolled trajectory,navigation trajectory and actual trajectory caused by initial state errors,and analyzes the reasons of producing the real engine-cutoff state deviations and fall point deviations in the case of guidance.Considering the modes of perturbation guidance and iterative guidance,analytical calculation approaches of guidance accuracy are proposed by introducing initial state errors.The approaches can be e mployed for continually compensating the flight state,thus improving the hit accuracy of the missile.Simulations indicate the effectiveness of the proposed analytical approach.Finally,the error propagation law based on covariance analysis describing equation technique(CADET)is studied.For the analysis of influence characteristics of a large number of initial state errors,Monte Carlo shooting method is generally used by a large amount of calculation through numerical integration.This will take a lot of calculation time and is not conducive to the rapid analysis of propagation characteristics.This paper proposes the employment of CADET to analyze error propagation characteristics.Statistical linearization is performed for nonlinear system,and the expressions of desired mean vector and dynamic matrix of quasilinear system are derived on the basis of normal distribution description function.Combined the dynamical equation of ballistic missile,mean and covariance propagation equations are established in the powered and unpowered phases.Simulations demonstrate the effectiveness of CADET.